you gotta go spelunking around for it (looking around for it) in the silph co building.
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The Card Key is found on the floor of the fifth floor of the Silph Co. building in Saffron City.
safron city
The Card Key is located on the Fifth floor in Silph Co. Clear at the bottom by a Rocket Grunt.
you will have to defeat Giovanni several times(In silph co. rocket hideout)
you go to fushia city to battle koga and claim your marsh badge